For discussion of all the other girl+mecha lines that have cropped up since Shinki began: Frame Arms: Girls, Megami Device, Armor Girls Project, Desktop Army, etc. This includes kinda-sortas like Daibadi's Polynian and things like Strike Witches and Fumikane's original Mecha Musume.

Hoihoi-san, I feel, is one of the design/concept ancestors of the Busou Shinki. She is ALSO a smol 1:1 action doll robot, only she comes from a dark future where cockroaches have become immune to common pesticides, and her job is to be the most adorable exterminator of these cursed roaches.

There's a whole manga about Hoihoi-san and the people who collect her kind (can be found on the Internet these days), and a short OVA that ties to the manga (can be found on Youtube these days).

I managed to get my hands on Hoihoi-san and Combat-san, and their size and styling is why I believe them to be the ancestors of our beloved shinki - They have SoC processor/storage setups like ultra-miniaturized PCs/Laptops, just like Shinki have a similar SoC processor array and SDcard support, and they have a charging stand system that predates the wireless induction chargers of the shinki (Voltage contacts in their feet). Unfortunately compared to shinki their computing power is so primitive they lack sapience and shinki-level autonomy, and they're treated more like appliances and dolls in their manga rather than like little companions like shinki.